Equivalent Definitions of A Closed Set
In a topological space, a set is closed if and only if it coincides with its closure. Equivalently, a set is closed if and only if it contains all of its limit points.
This is not to be confused with a closed manifold.
Read more about this topic: Closed Set
Famous quotes containing the words equivalent, definitions, closed and/or set:
“When the apple is ripe it will fall.”
—Irish proverb.
An English equivalent to this might be, “To everything there is a season.”
“The loosening, for some people, of rigid role definitions for men and women has shown that dads can be great at calming babies—if they take the time and make the effort to learn how. It’s that time and effort that not only teaches the dad how to calm the babies, but also turns him into a parent, just as the time and effort the mother puts into the babies turns her into a parent.”
—Pamela Patrick Novotny (20th century)
“Thus piteously Love closed what he begat:
The union of this ever-diverse pair!
These two were rapid falcons in a snare,
Condemned to do the flitting of the bat.”
—George Meredith (1828–1909)
“Mothers are not the nameless, faceless stereotypes who appear once a year on a greeting card with their virtues set to prose, but women who have been dealt a hand for life and play each card one at a time the best way they know how. No mother is all good or all bad, all laughing or all serious, all loving or all angry. Ambivalence rushes through their veins.”
—Erma Bombeck (20th century)